A simple algorithm to generate the minimal separators and the maximal cliques of a chordal graph
نویسندگان
چکیده
We present a simple unified algorithmic process which uses either LexBFS or MCS on a chordal graph to generate the minimal separators and the maximal cliques in linear time in a single pass.
منابع مشابه
Submission Track B : exact algorithm for Minimum Fill - In ( aka Chordal Completion )
Our implementation follows the exact algorithm of Fomin et al. [3] which is based on listing the minimal separators, the potential maximal cliques, and then performing dynamic programming based on those structures [1, 2]. The algorithm by Fomin et al. refines the approach of Bouchitté and Todinca on some minor aspects (only considering inclusion-minimal minimal separators, trying only the so-ca...
متن کاملComputing a clique tree with algorithm MLS (Maximal Label Search)
Algorithm MLS (Maximal Label Search) is a graph search algorithm which generalizes algorithmsMCS, LexBFS, LexDFS andMNS. On a chordal graph, MLS computes a peo (perfect elimination ordering) of the graph. We show how algorithm MLS can be modified to compute a pmo (perfect moplex ordering) as well as a clique tree and the minimal separators of a chordal graph. We give a necessary and sufficient ...
متن کاملComputing a Clique Tree with the Algorithm Maximal Label Search
The algorithm MLS (Maximal Label Search) is a graph search algorithm that generalizes the algorithms Maximum Cardinality Search (MCS), Lexicographic Breadth-First Search (LexBFS), Lexicographic Depth-First Search (LexDFS) and Maximal Neighborhood Search (MNS). On a chordal graph, MLS computes a PEO (perfect elimination ordering) of the graph. We show how the algorithm MLS can be modified to com...
متن کاملA Clique Tree Algorithm for Partitioning a Chordal Graph into Transitive Subgraphs
A partitioning problem on chordal graphs that arises in the solution of sparse triangular systems of equations on parallel computers is considered Roughly the problem is to partition a chordal graph G into the fewest transitively orientable subgraphs over all perfect elimination orderings of G subject to a certain precedence relationship on its vertices In earlier work a greedy scheme that solv...
متن کاملNew Tools and Results for Branchwidth
We provide new tools, such as k-troikas and good subtree-representations, that allow us to give fast and simple algorithms computing branchwidth. We show that a graph G has branchwidth at most k if and only if it is a subgraph of a chordal graph in which every maximal clique has a k-troika respecting its minimal separators. Moreover, if G itself is chordal with clique tree T then such a chordal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Inf. Process. Lett.
دوره 111 شماره
صفحات -
تاریخ انتشار 2011